Summary

A new numerical method is introduced that enables a reliable study of
disorder-induced localization of interacting particles. It is based on
a quantum mechanical time evolution calculation combined with a finite
size scaling analysis. The time evolution of up to four particles in
one dimension is studied and localization lengths are defined via the
long-time saturation values of the mean radius, the inverse
participation ratio and the center of mass extension. A systematic
study of finite size effects using the finite size scaling method is
performed in order to extract the localization lengths in the limit of
an infinite system size. For a single particle, the well-known scaling
of the localization length l1 with disorder strength W is observed, l1 ~ W-2. For two particles, an
interaction-induced delocalization is found, confirming previous
results obtained by numerically calculating matrix elements of the
two-particle Green's function: in the limit of small disorder, the
localization length increases with decreasing disorder as l2
~ W-4 and can be much larger than l1. For three
and four particles, delocalization is even stronger. Based on
analytical arguments, an upper bound for the n-particle localization
length ln is derived and shown to be in agreement with the
numerical data, ln ~l1^2n-1. Although the
localization length increases superexponentially with particle number
and can become arbitrarily large for small disorder, it does not
diverge for finite l1 and n. Hence, no extended
states exist in one dimension, at least for spinless
fermions.